Multivariate extension of the tropical-polynomial results

Extend the structural, algorithmic, and algebraic results for univariate tropical polynomials to multivariate tropical polynomials.

Background

The paper's theory is developed for tropical polynomials in one variable, including tropical decomposition width, modular convexity, interpolation algebras, and convolution algorithms. The authors ask whether these results extend to the multivariate setting, which they associate with lattice theory and discrete convex analysis.